Embed Size (px)
Citation preview
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Unit 1: Congruence, Proof, and Constructions Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP1-Week1 Length: 7-8 Weeks Status: Published Unit Overview
Summary
Critical Area 1: In previous grades, students were asked to draw triangles based on given measurements.
They also have prior experience with rigid motions: translations, reflections, and rotations and have used
these to develop notions about what it means for two objects to be congruent. In this unit, students
establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use
triangle congruence as a familiar foundation for the development of formal proof. Students prove
theorems—using a variety of formats—and solve problems about triangles, quadrilaterals, and other
polygons. They apply reasoning to complete geometric constructions and explain why they work.
(Common Core State Standards for Mathematics: Appendix A, p. 27)
Interdisciplinary Connections
Technology, 21st Century Life and Careers
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Rationale
The content presented in this unit works in tandem with the Standards for Mathematical Practice. These practices in
addition to the content standards address help to provide students with exposure to ‐‐ in short ‐‐ solve problems. The
world is constantly evolving and changing, but one thing remains true, there are always problems to solve. Exposure
to mathematical practices through the content standards will build a stronger foundation upon which students can
continue to learn, grow and succeed in an ever changing global society.
MA.K‐12.MP.1 Make sense of problems and persevere in solving them. MA.K‐12.MP.2 Reason abstractly and quantitatively. MA.K‐12.MP.3 Construct viable arguments and critique the reasoning of others. MA.K‐12.MP.4 Model with mathematics. MA.K‐12.MP.5 Use appropriate tools strategically. MA.K‐12.MP.6 Attend to precision. MA.K‐12.MP.7 Look for and make use of structure. MA.K‐12.MP.8 Look for and express regularity in repeated reasoning.
21st Century Components
21st Century Themes
Global Awareness
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Environmental Literacy
Civic Literacy
Health Literacy
Financial, Economic, Business, and Entrepreneurial Literacy
21st Century Skills
X Creative & Innovative
X Critical Thinking & Problem Solving
X Communication & Collaboration
Information Literacy
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Media Literacy
ICT Literacy
Life & Career Skills
Integration of Technology
Graphing Calculators
Geometer's Sketchpad
Holt McDougal Online
Math Videos for reinforcement
ActiVotes
blogs as math journals
wikis as how‐to and quick references
glogster as informational posters
Learning Targets
The following are the NJ state standards in the main content area being addressed by this unit.
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
MA.9‐12.HSG‐CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
MA.9‐12.HSG‐CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
MA.9‐12.HSG‐CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
MA.9‐12.HSG‐CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
MA.9‐12.HSG‐CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
MA.9‐12.HSG‐CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
MA.9‐12.HSG‐CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
MA.9‐12.HSG‐CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
MA.9‐12.HSG‐CO.9 Prove theorems about lines and angles. MA.9‐12.HSG‐CO.10 Prove theorems about triangles. MA.9‐12.HSG‐CO.11 Prove theorems about parallelograms. MA.9‐12.HSG‐CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string,
reflective devices, paper folding, dynamic geometric software, etc.). MA.9‐12.HSG‐CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Learning Expectations
Essential Questions
What is the value of studying Geometry?
What couldn’t we do if we didn’t understand visualization skills?
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
How are inductive and deductive reasoning used in the real world?
Enduring Understandings
Students will understand...
the choice of notation and/or terms determines meaning
mathematical symbols replace words in mathematical sentences
inductive and deductive reasoning accomplish different goals
SSS, SAS, SAA, and ASA are triangle congruence shortcuts, but SSA and AAA are not
equilateral triangles are equiangular and vice versa
Learning Expectations (Knowledge) Students will know...
the terminology and notation associated with geometric objects
the relationships between special pairs of angles
the relationships of angles formed by a transversal cutting parallel lines
the history of geometric constructions
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
the difference between sketching, drawing, and geometric construction
the choice of notation and/or terms determines meaning
mathematical symbols replace words in mathematical sentences
inductive and deductive reasoning accomplish different goals
the sum of the measures of the interior and exterior angles of a polygon
the relationships between sides of a triangle and the angles opposite them and vice versa
the sum of the lengths of any two sides of a triangle is greater than the third side
the measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles
the properties the symmetry line in an isosceles triangle
Learning Expectations (Ability) Students will be able to...
identify, name, and draw points, lines segments, rays and planes
apply basic facts about points, lines and planes
measure distances and explore properties of points on segments
use length and midpoint of a segment
construct midpoints and congruent segments
name and classify angles
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
measure and construct angles and angle bisectors
identify adjacent, vertical, complementary and supplementary angles
find measures of pairs of angles
apply formulas for perimeter, area, and circumference
develop and apply the formula for midpoint
use the Distance Formula and the Pythagorean Theorem to find the distance between two points
identify reflections, rotations and translations
graph transformations in the coordinate plane
perform transformations and explore their properties
use inductive reasoning to identify patterns and make conjectures
find counterexample to disprove conjectures
identify, write, and analyze the truth value of conditional statements
write the inverse, converse, and contrapositive of a conditional statement
apply the Law of Detachment and the Law of Syllogism in logical reasoning
use tables to solve logic problems
use networks to solve logic problems
write and analyze biconditional statements
review properties of equality and use them to write algebraic proofs
identify properties of equality and congruence
write two‐column proofs
prove geometric theorems by using deductive reasoning
learn strategies for planning the logical steps of proof
write flowchart and paragraph proofs
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
prove geometric theorems by using deductive reasoning
analyze the truth value of conjunctions and disjunctions
construct truth tables to determine the truth value of logical statements
identify parallel, perpendicular, and skew lines
identify the angles formed by two lines and a transversal
explore angles formed by parallel lines and transversals
prove and use theorems about the angles formed by parallel lines and a transversal
use the angles formed by a transversal to prove two lines are parallel
use various methods to construct parallel lines
prove and apply theorems about perpendicular lines
construct a line perpendicular to a give line through a given point
draw, identify and describe transformations in the coordinate plane
use properties of rigid motions to determine whether figures are congruent and to prove figures
congruent
classify triangle by their angle measures and side lengths
use triangle classification to find angle measures and side lengths
discover the relationship between the measures of the interior angles of a triangle
find the measures of interior and exterior angles of triangles
apply theorems about the interior and exterior angles of triangles
use properties of congruent triangles
prove triangles congruent by using the definition of congruency
discover shortcuts for proving triangles congruent
apply SSS and SAS to construct triangles and solve problems
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
prove triangles congruent by using SSS and SAS
explore triangle congruence relationships
apply ASA, AAS, and HL to construct triangle and solve problems
prove triangles congruent by using ASA, AAS, and HL
use CPCTC to prove parts of triangle are congruent
prove the slope criteria for parallel and perpendicular lines
position figures in the coordinate plane for use in coordinate proofs
prove geometric concepts by using the coordinate proofs
prove theorems about isosceles and equilateral triangles
apply properties of isosceles and equilateral triangles
use congruent triangles to prove constructions valid
use a compass and straightedge to construct regular polygons
classify polygons based on their sides and angles
find and use the measures of interior and exterior angles of polygons
explore properties of parallelograms
prove and apply properties of parallelograms
use properties of parallelograms to solve problems
prove that a given quadrilateral is a parallelogram
prove and apply properties of rectangles, rhombuses, and squares
use properties of rectangles, rhombuses, and squares to solve problems
prove that a given quadrilateral is a rectangle, rhombus, or square
investigate the properties and conditions of an isosceles trapezoid
use properties of kites to solve problems
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
use properties of trapezoids to solve problems
Evidence of Learning
Formative Assessments
From Holt McDougal Geometry, Common Core Edition ©2013
Are You Ready?
Warm Up
Check It Out!
Think and Discuss
Write About It
Journal
Lesson Quiz
Test Prep
Ready to Go On?
Section Quizzes
College Entrance Exam Practice
Standardized Test Prep
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Teacher/District Created
ECR questions
MAP (Measures of Academic Progress)
Self and peer assessments
Communicators
Activote quizzes
Teacher created materials
Math journals
Graphic organizers
Teacher observations
Peer interaction
Do Nows & Exit Tickets
District formative assessments
Summative Assessments
End of Chapter Assessments
Teacher Designed Tests
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Modifications & Other Resources
Instructional Resources/Notes
Holt McDougal Geometry, Common Core Edition ©2012
o Chapter 1
o Chapter 2
o Chapter 3: Sections 1‐4 (Lines with Transversals)
o Chapter 4
o Chapter 6
Ohio Model Curricula (The current focus of this document is to provide instructional strategies and resources,
and identify misconceptions and connections related to the clusters and standards)
o Number and Quantity
o Algebra
o Functions
o Geometry
o Statistics & Probability
Decartes (utilizing MAP RIT ranges for each cluster)
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Curriculum Development Resources
Holt McDougal Geometry, Common Core Edition ©2012
Common Core State Standards for Mathematics
Common Core State Standards for Mathematics: Appendix A
Model Curriculum: K‐12
Timeline for Model Curriculum
Unit 2: Similarity, Proof, and Trigonometry Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP1-Week9 Length: 7-8 Weeks Status: Published Unit Overview
Summary
Critical Area 2: Students apply their earlier experience with dilations and proportional reasoning to build a
formal understanding of similarity. They identify criteria for similarity of triangles, use similarity to solve
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
problems, and apply similarity in right triangles to understand right triangle trigonometry, with particular
attention to special right triangles and the Pythagorean theorem. Students develop the Laws of Sines and
Cosines in order to find missing measures of general (not necessarily right) triangles, building on students’
work with quadratic equations done in the first course. They are able to distinguish whether three given
measures (angles or sides) define 0, 1, 2, or infinitely many triangles.
(Common Core State Standards for Mathematics: Appendix A, p. 27)
Interdisciplinary Connections
Technology, 21st Century Life and Careers
Rationale
The content presented in this unit works in tandem with the Standards for Mathematical Practice. These practices in
addition to the content standards address help to provide students with exposure to ‐‐ in short ‐‐ solve problems. The
world is constantly evolving and changing, but one thing remains true, there are always problems to solve. Exposure
to mathematical practices through the content standards will build a stronger foundation upon which students can
continue to learn, grow and succeed in an ever changing global society.
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
MA.K‐12.MP.1 Make sense of problems and persevere in solving them. MA.K‐12.MP.2 Reason abstractly and quantitatively. MA.K‐12.MP.3 Construct viable arguments and critique the reasoning of others. MA.K‐12.MP.4 Model with mathematics. MA.K‐12.MP.5 Use appropriate tools strategically. MA.K‐12.MP.6 Attend to precision. MA.K‐12.MP.7 Look for and make use of structure. MA.K‐12.MP.8 Look for and express regularity in repeated reasoning.
21st Century Components
21st Century Themes
Global Awareness
Environmental Literacy
Civic Literacy
Health Literacy
Financial, Economic, Business, and Entrepreneurial Literacy
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
21st Century Skills
X Creative & Innovative
X Critical Thinking & Problem Solving
X Communication & Collaboration
Information Literacy
Media Literacy
ICT Literacy
Life & Career Skills
Integration of Technology
Graphing Calculators
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Geometer's Sketchpad
Holt McDougal Online
Math Videos for reinforcement
ActiVotes
blogs as math journals
wikis as how‐to and quick references
glogster as informational posters
Learning Targets
The following are the NJ state standards in the main content area being addressed by this unit.
MA.9‐12.HSG‐SRT.1.a A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
MA.9‐12.HSG‐SRT.1.b The dilation of a line segment is longer or shorter in the ratio given by the scale factor. MA.9‐12.HSG‐SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are
similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
MA.9‐12.HSG‐SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. MA.9‐12.HSG‐SRT.4 Prove theorems about triangles. MA.9‐12.HSG‐SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric
figures. MA.9‐12.HSG‐SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading
to definitions of trigonometric ratios for acute angles. MA.9‐12.HSG‐SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. MA.9‐12.HSG‐SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. MA.9‐12.HSG‐SRT.9 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side.
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
MA.9‐12.HSG‐SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems. MA.9‐12.HSG‐SRT.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and
non‐right triangles (e.g., surveying problems, resultant forces). MA.9‐12.HSG‐MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a
human torso as a cylinder). MA.9‐12.HSG‐MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile,
BTUs per cubic foot). MA.9‐12.HSG‐MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical
constraints or minimize cost; working with typographic grid systems based on ratios).
Learning Expectations
Essential Questions
What kinds of symmetry do we see in nature and artificial objects?
How do units of measurement affect area?
How does the area change if a shape is cut into pieces that are rearranged to make a different shape?
Why is the Pythagorean Theorem one of the most important discoveries in mathematics?
What makes a proof correct? What makes a proof elegant?
Enduring Understandings
Students will understand...
the Pythagorean Theorem can be used to find the distance between two points
similar figures have proportional sides and congruent angles
proving theorems is an art, not an algorithm
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Learning Expectations (Knowledge) Students will know...
vector notation
how to identify transformations
how to classify and identify tessellations (monohedral, regular, and semi‐regular)
area formulas
the Pythagorean Theorem
how to create Escher‐type tessellations with translations, rotations, and reflections
how to derive and apply the sine, cosine and tangent ratios
derive and apply the Law of Sines and Law of Cosines
the definitions of similar polygons, similar triangles
the critical components of a good proof
how to use proportions to find measures in similar figures
Learning Expectations (Ability) Students will be able to...
prove and apply theorems about perpendicular bisectors
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
prove and apply theorems about angle bisectors
prove and apply properties of perpendicular bisectors of a triangle
prove and apply properties of angle bisectors of a triangle
apply properties of medians of a triangle
apply properties of altitudes of a triangle
use special points in triangles to explore Euler’s line
prove and use properties of triangle midsegments
explore the relationships between side lengths and angle measures in a triangle
write indirect proofs
apply inequalities in one triangle
apply inequalities in two triangles
use area to justify the Pythagorean Theorem
use the Pythagorean Theorem and its converse to solve problems
use Pythagorean inequalities to classify triangles
justify and apply properties of 45˚‐45˚‐90˚ triangles
justify and apply properties of 30˚‐60˚‐90˚ triangles
graph irrational numbers on a number line
identify similar polygons
apply properties of similar polygons to solve problems
draw and describe similarity transformations in the coordinate plane
use properties of similarity transformations to determine whether polygons are similar and to prove
circles similar
find ways to determine that triangle are similar
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
prove certain triangles are similar by using AA, SSS, and SAS
use triangle similarity to solve problems
prove the Pythagorean Theorem using similar triangles
explore the relationship between the two segments into which an angle bisector divides the opposite
side of a triangle
use properties of similar triangles to find segment lengths
apply proportionality and triangle angle bisector theorems
use ratios to make indirect measurements
use scale drawings to solve problems
apply similarity properties in the coordinate plane
use coordinate proof to prove figures similar
divide a directed line segment into partitions
use geometric mean to find segment lengths in right triangles
apply similarity relationships in right triangles to solve problems
explore trigonometric ratios in right triangles
find the sine, cosine, and tangent of an acute angle
use trigonometric ratios to find side lengths in right triangles and to solve real‐world problems
use the relationship between the sine and cosine of complementary angles
use trigonometric ratios to find angle measures in right triangles and to solve real‐world problems
solve problems involving angles of elevation and angles of depression
make a clinometers and use trigonometry to measure objects indirectly
use the Law of Sines and the Law of Cosines to solve triangles
find the magnitude and direction of a vector
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
use vectors and vector addition to solve real‐world problems
define trigonometric ratios for angle measures greater than or equal to 90˚
identify and draw reflections
identify and draw translations
identify and draw rotations
explore transformations with matrices
apply theorems about isometrics
identify and draw compositions of transformations, such as glide reflections
identify and describe symmetry in geometric figures
understand how solids can be produced by rotating a two‐dimensional figure through space
use transformations to draw tessellations
identify regular and semiregular tessellations and figures that will tessellate
identify and draw dilations
describe iterative patterns that generate fractals
Evidence of Learning
Formative Assessments
From Holt McDougal Geometry, Common Core Edition ©2013
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Are You Ready?
Warm Up
Check It Out!
Think and Discuss
Write About It
Journal
Lesson Quiz
Test Prep
Ready to Go On?
Section Quizzes
College Entrance Exam Practice
Standardized Test Prep
Teacher/District Created
ECR questions
MAP (Measures of Academic Progress)
Self and peer assessments
Communicators
Activote quizzes
Teacher created materials
Math journals
Graphic organizers
Teacher observations
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Peer interaction
Do Nows & Exit Tickets
District formative assessments
Summative Assessments
End of Chapter Assessments
Teacher Designed Tests
Modifications & Other Resources
Instructional Resources/Notes
Holt McDougal Geometry, Common Core Edition ©2012
o Chapter 5
o Chapter 7
o Chapter 8
o Chapter 9
Ohio Model Curricula (The current focus of this document is to provide instructional strategies and resources,
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
and identify misconceptions and connections related to the clusters and standards)
o Number and Quantity
o Algebra
o Functions
o Geometry
o Statistics & Probability
Decartes (utilizing MAP RIT ranges for each cluster)
Curriculum Development Resources
Holt McDougal Geometry, Common Core Edition ©2012
Common Core State Standards for Mathematics
Common Core State Standards for Mathematics: Appendix A
Model Curriculum: K‐12
Timeline for Model Curriculum
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Unit 3: Extending to Three Dimensions Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP2-Week7 Length: 7-8 Weeks Status: Published Unit Overview
Summary
Critical Area 3: Students’ experience with two‐dimensional and three‐dimensional objects is extended to
include
informal explanations of circumference, area and volume formulas. Additionally, students apply their
knowledge of two‐dimensional shapes to consider the shapes of cross‐sections and the result of rotating a
two‐dimensional object about a line.
(Common Core State Standards for Mathematics: Appendix A, p. 27)
Interdisciplinary Connections
Technology, 21st Century Life and Careers
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Rationale
The content presented in this unit works in tandem with the Standards for Mathematical Practice. These practices in
addition to the content standards address help to provide students with exposure to ‐‐ in short ‐‐ solve problems. The
world is constantly evolving and changing, but one thing remains true, there are always problems to solve. Exposure
to mathematical practices through the content standards will build a stronger foundation upon which students can
continue to learn, grow and succeed in an ever changing global society.
MA.K‐12.MP.1 Make sense of problems and persevere in solving them. MA.K‐12.MP.2 Reason abstractly and quantitatively. MA.K‐12.MP.3 Construct viable arguments and critique the reasoning of others. MA.K‐12.MP.4 Model with mathematics. MA.K‐12.MP.5 Use appropriate tools strategically. MA.K‐12.MP.6 Attend to precision. MA.K‐12.MP.7 Look for and make use of structure. MA.K‐12.MP.8 Look for and express regularity in repeated reasoning.
21st Century Components
21st Century Themes
Global Awareness
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Environmental Literacy
Civic Literacy
Health Literacy
Financial, Economic, Business, and Entrepreneurial Literacy
21st Century Skills
X Creative & Innovative
X Critical Thinking & Problem Solving
X Communication & Collaboration
Information Literacy
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Media Literacy
ICT Literacy
Life & Career Skills
Integration of Technology
Graphing Calculators
Geometer's Sketchpad
Holt McDougal Online
Math Videos for reinforcement
ActiVotes
blogs as math journals
wikis as how‐to and quick references
glogster as informational posters
Learning Targets
The following are the NJ state standards in the main content area being addressed by this unit.
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
MA.9‐12.HSG‐GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
MA.9‐12.HSG‐GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. MA.9‐12.HSG‐GMD.4 Identify the shapes of two‐dimensional cross‐sections of three‐dimensional objects, and identify three‐
dimensional objects generated by rotations of two‐dimensional objects. MA.9‐12.HSG‐MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a
human torso as a cylinder).
Learning Expectations
Essential Questions
How can you find the volume of solids for which no formula is available?
Liquid medications are dosed in cubic centimeters: why don’t I need a cube to measure the dose?
Enduring Understandings
Students will understand...
π is the ratio of the circumference of a circle to its diameter
volume is conserved (e.g. doubling the radius and dividing the height of a cylinder by four does not change the
volume)
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Learning Expectations (Knowledge) Students will know...
the vocabulary of solids: polyhedrons (including prisms and pyramids), cylinders, cones, and spheres
volume formulas
how to find volumes of irregularly shaped solids through displacement or density
how to derive and apply the formulas for the volume and surface area of a sphere
Learning Expectations (Ability) Students will be able to...
develop and apply the formulas for the areas of triangles and special quadrilaterals
solve problems involving perimeters and areas of triangles and special quadrilaterals
use construction and measurement to develop π
develop and apply the formulas for the area and circumference of a circle
develop and apply the formula for the area of a regular polygon
use the Area Addition Postulate to find the areas of composite figures
use composite figures to estimate the areas of irregular shapes
find the perimeters and areas of figures in a coordinate plane
describe the effect on perimeter and area when one or more dimension of a figure are changed
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
apply the relationship between perimeter and area in problem solving
calculate geometric probabilities
use geometric probability to predict results in real‐world situations
use geometric probability to estimate π
classify three‐dimensional figures according to their properties
use nets and cross sections to analyze three‐dimensional figures
learn and apply the formula for volume of a prism
learn and apply the formula for volume of a cylinder
learn and apply the formula for volume of a pyramid
learn and apply the formula for volume of a cone
learn and apply the formula for volume of a sphere
learn and apply the formula for surface area of a sphere
compare and contract surface areas and volumes
Evidence of Learning
Formative Assessments
From Holt McDougal Geometry, Common Core Edition ©2013
Are You Ready?
Warm Up
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Check It Out!
Think and Discuss
Write About It
Journal
Lesson Quiz
Test Prep
Ready to Go On?
Section Quizzes
College Entrance Exam Practice
Standardized Test Prep
Teacher/District Created
ECR questions
MAP (Measures of Academic Progress)
Self and peer assessments
Communicators
Activote quizzes
Teacher created materials
Math journals
Graphic organizers
Teacher observations
Peer interaction
Do Nows & Exit Tickets
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
District formative assessments
Summative Assessments
End of Chapter Assessments
Teacher Designed Tests
Modifications & Other Resources
Instructional Resources/Notes
Holt McDougal Geometry, Common Core Edition ©2012
o Chapter 10
o Chapter 11
Ohio Model Curricula (The current focus of this document is to provide instructional strategies and resources,
and identify misconceptions and connections related to the clusters and standards)
o Number and Quantity
o Algebra
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
o Functions
o Geometry
o Statistics & Probability
Decartes (utilizing MAP RIT ranges for each cluster)
Curriculum Development Resources
Holt McDougal Geometry, Common Core Edition ©2012
Common Core State Standards for Mathematics
Common Core State Standards for Mathematics: Appendix A
Model Curriculum: K‐12
Timeline for Model Curriculum
Unit 4: Connecting Algebra and Geometry through Coordinates
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP3-Week5 Length: 3-4 Weeks Status: Published Unit Overview
Summary
Critical Area 4: Building on their work with the Pythagorean theorem in 8th grade to find distances, students
use a rectangular coordinate system to verify geometric relationships, including properties of special
triangles and quadrilaterals and slopes of parallel and perpendicular lines, which relates back to work done in
the first course. Students continue their study of quadratics by connecting the geometric and algebraic
definitions of the parabola.
(Common Core State Standards for Mathematics: Appendix A, p. 27)
Interdisciplinary Connections
Technology, 21st Century Life and Careers
Rationale
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
The content presented in this unit works in tandem with the Standards for Mathematical Practice. These practices in
addition to the content standards address help to provide students with exposure to ‐‐ in short ‐‐ solve problems. The
world is constantly evolving and changing, but one thing remains true, there are always problems to solve. Exposure
to mathematical practices through the content standards will build a stronger foundation upon which students can
continue to learn, grow and succeed in an ever changing global society.
MA.K‐12.MP.1 Make sense of problems and persevere in solving them. MA.K‐12.MP.2 Reason abstractly and quantitatively. MA.K‐12.MP.3 Construct viable arguments and critique the reasoning of others. MA.K‐12.MP.4 Model with mathematics. MA.K‐12.MP.5 Use appropriate tools strategically. MA.K‐12.MP.6 Attend to precision. MA.K‐12.MP.7 Look for and make use of structure. MA.K‐12.MP.8 Look for and express regularity in repeated reasoning.
21st Century Components
21st Century Themes
Global Awareness
Environmental Literacy
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Civic Literacy
Health Literacy
Financial, Economic, Business, and Entrepreneurial Literacy
21st Century Skills
X Creative & Innovative
X Critical Thinking & Problem Solving
X Communication & Collaboration
Information Literacy
Media Literacy
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
ICT Literacy
Life & Career Skills
Integration of Technology
Graphing Calculators
Geometer's Sketchpad
Holt McDougal Online
Math Videos for reinforcement
ActiVotes
blogs as math journals
wikis as how‐to and quick references
glogster as informational posters
Learning Targets
The following are the NJ state standards in the main content area being addressed by this unit.
MA.9‐12.HSG‐GPE.2 Derive the equation of a parabola given a focus and directrix.
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
MA.9‐12.HSG‐GPE.4 Use coordinates to prove simple geometric theorems algebraically. MA.9‐12.HSG‐GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g.,
find the equation of a line parallel or perpendicular to a given line that passes through a given point). MA.9‐12.HSG‐GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given
ratio. MA.9‐12.HSG‐GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the
distance formula.
Learning Expectations
Essential Questions
Enduring Understandings
Students will understand...
the relationship between two lines can be determined by comparing their slopes and y‐intercepts
all mathematical subjects are interrelated to one another
the type of slope can be assessed simply by looking at the direction of the line: diagonal up, diagonal down,
horizontal and vertical
Learning Expectations (Knowledge)
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Students will know...
there are three basic relationships between lines: parallel, intersecting, and coinciding
that when two line intersect at right angles they are perpendicular
the relationship between the slopes of parallel lines and of perpendicular lines
the product of the slopes of two perpendicular lines is ‐1
there are four types of slope: positive, negative, zero, and undefined
the formula for slope
what point‐slope form and slope‐intercept form looks like
slope‐intercept form is best when trying to identify the slope and y‐intercept and when wishing to graph a line
point‐slope form is typically the best when trying to find the equation of a line given a point and slope or given
two points
Learning Expectations (Ability) Students will be able to...
find the slope of a line
use slope to identify parallel and perpendicular lines
graph lines, and write their equations in slope‐intercept and point‐slope form
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
classify lines as parallel, intersecting or coinciding
Evidence of Learning
Formative Assessments
From Holt McDougal Geometry, Common Core Edition ©2013
Are You Ready?
Warm Up
Check It Out!
Think and Discuss
Write About It
Journal
Lesson Quiz
Test Prep
Ready to Go On?
Section Quizzes
College Entrance Exam Practice
Standardized Test Prep
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Teacher/District Created
ECR questions
MAP (Measures of Academic Progress)
Self and peer assessments
Communicators
Activote quizzes
Teacher created materials
Math journals
Graphic organizers
Teacher observations
Peer interaction
Do Nows & Exit Tickets
District formative assessments
Summative Assessments
End of Chapter Assessments
Teacher Designed Tests
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Modifications & Other Resources
Instructional Resources/Notes
Holt McDougal Geometry, Common Core Edition ©2012
o Chapter 3: Sections 5‐6 (Coordinate Geometry)**
o ** Need to pull outside resources to supplement in order to fully cover CCSS **
Ohio Model Curricula (The current focus of this document is to provide instructional strategies and resources,
and identify misconceptions and connections related to the clusters and standards)
o Number and Quantity
o Algebra
o Functions
o Geometry
o Statistics & Probability
Decartes (utilizing MAP RIT ranges for each cluster)
Curriculum Development Resources
Holt McDougal Geometry, Common Core Edition ©2012
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Common Core State Standards for Mathematics
Common Core State Standards for Mathematics: Appendix A
Model Curriculum: K‐12
Timeline for Model Curriculum
Unit 5: Circles With and Without Coordinates Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP3-Week8 Length: 3-4 Weeks Status: Published Unit Overview
Summary
Critical Area 5: In this unit students prove basic theorems about circles, such as a tangent line is
perpendicular to a radius, inscribed angle theorem, and theorems about chords, secants, and tangents
dealing with segment lengths and angle measures. They study relationships among segments on chords,
secants, and tangents as an application of similarity. In the Cartesian coordinate system, students use the
distance formula to write the equation of a circle when given the radius and the coordinates of its center.
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving
quadratic equations, which relates back to work done in the first course, to determine intersections between
lines and circles or parabolas and between two circles.
(Common Core State Standards for Mathematics: Appendix A, p. 27)
Interdisciplinary Connections
Technology, 21st Century Life and Careers
Rationale
The content presented in this unit works in tandem with the Standards for Mathematical Practice. These practices in
addition to the content standards address help to provide students with exposure to ‐‐ in short ‐‐ solve problems. The
world is constantly evolving and changing, but one thing remains true, there are always problems to solve. Exposure
to mathematical practices through the content standards will build a stronger foundation upon which students can
continue to learn, grow and succeed in an ever changing global society.
MA.K‐12.MP.1 Make sense of problems and persevere in solving them. MA.K‐12.MP.2 Reason abstractly and quantitatively. MA.K‐12.MP.3 Construct viable arguments and critique the reasoning of others. MA.K‐12.MP.4 Model with mathematics.
Unit 6: Applications of Probability Content Area: Mathematics Course(s): Geometry Honors, Geometry Time Period: MP4-Week2 Length: 7 Weeks Status: Published Unit Overview
Summary
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages
of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for
compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
(Common Core State Standards for Mathematics: Appendix A, p27)
Interdisciplinary Connections
MA.K‐12.MP.5 Use appropriate tools strategically. MA.K‐12.MP.6 Attend to precision. MA.K‐12.MP.7 Look for and make use of structure. MA.K‐12.MP.8 Look for and express regularity in repeated reasoning.
21st Century Components
![Analysis, Probability, ' }u Çv o] }v NONLOCAL OPERATORSNonlocalOperators Analysis, Probability, Geometry and Applications CenterforInterdisciplinaryResearch(ZiF),Bielefeld July9–14,2012](https://img.dokumen.tips/doc/110x75/5ee058ebad6a402d666b8c35/analysis-probability-u-v-o-v-nonlocal-operators-nonlocaloperators-analysis.jpg)
